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# Managerial Finance

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Discussion Question 1:
Many people, as evidenced by the large payoffs provided for picking 6 out of 53 (or more) numbers, play the lottery. The big choice the winners face: taking a lump sum payment today or an annual payment over 20 years. Is a dollar today worth more than a dollar tomorrow? Why or why not? Which do you prefer, the lump sum or the 20 year payment stream?

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This question involves the fundamentals of managerial finance.

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If we knew how to pick winning numbers, kid, we wouldn't be writing these reports, we'd be enjoying life on South Seas cruises. Cecil has already explained the problem.

The question of which is better, cash value or annual payments, doesn't depend on the jackpot amount; it depends on the interest rate reflected in the annual payment. Since lottery rules are different in every state, I'm going to provide a general overview that works in every state, and caution you about what might be different in particular lotteries.

First some terms. An annuity is a series of annual payments (usually of equal size) over some period of time. There are different kinds of annuities, such as an annuity certain where the payments are made for a fixed number of years, or a life annuity where the payments are made for the lifetime of an individual. Most state lotteries offer an annuity certain.

The face value of an annuity is the payment amount times the number of payments. In a lottery, the face value is the amount advertised on the billboards - "this week's jackpot is \$X million!" - although nobody ever gets all the money at one time. The cash value or present value of an annuity is the amount of money, today, that is mathematically equivalent to the sum of the payments, given a particular interest rate. By equivalent I mean that, if you deposited the cash value in an account bearing the agreed-upon interest rate for the term of the annuity, the accumulated amount would equal the face value.

In a typical state lottery, the cash value is roughly half the face value. Modern lotteries, you see, involve a bit of financial sleight of hand. You've "won" \$X million only in the sense that you'll receive that much if you're willing to wait 20 years to collect it. What you've actually won is the cash value plus the interest that accumulates.
The assumption underlying most annuities is that money is constantly productive - that is, there is a time-value to money, represented mathematically as the interest rate. The interest rate is critical in determining whether a lump sum is a better deal than an annuity.

To put ...

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